A098365 -id:A098365 - cp's OEIS frontend

A099178 Numbers which are the sum of two positive cubes and divisible by 17.

1241, 1343, 1547, 1853, 2261, 2771, 3383, 4097, 9826, 9928, 10234, 10744, 11458, 12376, 13498, 14824, 16354, 18088, 20026, 22168, 24514, 27064, 29818, 32776, 33201, 33507, 34119, 35037, 35938, 36261, 37791, 39627, 41769, 44217, 46971

Offset: 1

Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Nov 15 2004

			Sums not divisible by 17 are indicated in asterisks:
....|...1....8...27...64...125...216...343...512...729..1000..1331
------------------------------------------------------------------
1...|...*....*....*....*.....*.....*.....*.....*.....*.....*.....*
8...|...*....*....*....*.....*.....*.....*.....*.....*.....*.....*
27..|...*....*....*....*.....*.....*.....*.....*.....*.....*.....*
64..|...*....*....*....*.....*.....*.....*.....*.....*.....*.....*
125.|...*....*....*....*.....*.....*.....*.....*.....*.....*.....*
216.|...*....*....*....*.....*.....*.....*.....*.....*.....*..1547
343.|...*....*....*....*.....*.....*.....*.....*.....*..1343.....*
512.|...*....*....*....*.....*.....*.....*.....*...1241....*.....*
729.|...*....*....*....*.....*.....*.....*..1241.....*.....*.....*
1000|...*....*....*....*.....*.....*..1343.....*.....*.....*.....*
1331|...*....*....*....*.....*..1547.....*.....*.....*.....*.....*

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A098365.

upto[n_] := Block[{t}, Union@ Reap[ Do[If[Mod[t = x^3 + y^3, 17] == 0, Sow@t], {x, n^(1/3)}, {y, Min[x, (n - x^3)^(1/3)]}]][[2, 1]]]; upto[47000] (* Giovanni Resta, Jun 12 2020 *)

A098364 Multiplication table of the digits of the square root of 2 read by antidiagonals.

Original entry on oeis.org

1, 4, 4, 1, 16, 1, 4, 4, 4, 4, 2, 16, 1, 16, 2, 1, 8, 4, 4, 8, 1, 3, 4, 2, 16, 2, 4, 3, 5, 12, 1, 8, 8, 1, 12, 5, 6, 20, 3, 4, 4, 4, 3, 20, 6, 2, 24, 5, 12, 2, 2, 12, 5, 24, 2, 3, 8, 6, 20, 6, 1, 6, 20, 6, 8, 3, 7, 12, 2, 24, 10, 3, 3, 10, 24, 2, 12, 7, 3, 28, 3, 8, 12, 5, 9, 5, 12, 8, 3, 28, 3

Offset: 1

Douglas Stones (dssto1(AT)student.monash.edu.au), Sep 04 2004

			Triangle begins:
  1;
  4,4;
  1,16,1;
  4,4,4,4;
  ...
Array begins:
  1  4 1  4 2 ...
  4 16 4 16 8 ...
  1  4 1  4 2 ...
  4 16 4 16 8 ...
  2  8 2  8 4 ...
  ...

Michel Marcus, Antidiagonals n = 1..100, flattened

Cf. A002193, A003991, A098365, A098366, A098367.

sqrt2(nn) = {my(r=0, x=2, list = List(), d); for(digits=1, nn, d=0; while((20*r+d)*d <= x, d++); d--; listput(list, d); x=100*(x-(20*r+d)*d); r=10*r+d;); Vec(list);} \\ A002193
lista(nn) = {my(dd = sqrt2(nn)); for (n=1, nn, for (k=1, n, print1(dd[k]*dd[n-k+1], ", ")));} \\ Michel Marcus, Nov 11 2021

T(n,k) = A003991(A002193(n), A002193(k)). - Michel Marcus, Nov 03 2021

Offset changed to 1 and a(34)=1 inserted by Georg Fischer, Nov 02 2021

A098366 Multiplication table of the digits of the cube root of 2 read by antidiagonals.

Original entry on oeis.org

1, 2, 2, 5, 4, 5, 9, 10, 10, 9, 9, 18, 25, 18, 9, 2, 18, 45, 45, 18, 2, 1, 4, 45, 81, 45, 4, 1, 0, 2, 10, 81, 81, 10, 2, 0, 4, 0, 5, 18, 81, 18, 5, 0, 4, 9, 8, 0, 9, 18, 18, 9, 0, 8, 9, 8, 18, 20, 0, 9, 4, 9, 0, 20, 18, 8, 9, 16, 45, 36, 0, 2, 2, 0, 36, 45, 16, 9, 4, 18, 40, 81, 36, 0, 1, 0, 36

Offset: 0

Douglas Stones (dssto1(AT)student.monash.edu.au), Sep 04 2004

			1; 2,2; 5,4,5; 9,10,10,9; ...

Cf. A003991, A098364, A098365, A098367.

A098367 Multiplication table of the digits of the fourth root of 2 read by antidiagonals.

Original entry on oeis.org

1, 1, 1, 8, 1, 8, 9, 8, 8, 9, 2, 9, 64, 9, 2, 0, 2, 72, 72, 2, 0, 7, 0, 16, 81, 16, 0, 7, 1, 7, 0, 18, 18, 0, 7, 1, 1, 1, 56, 0, 4, 0, 56, 1, 1, 5, 1, 8, 63, 0, 0, 63, 8, 1, 5, 0, 5, 8, 9, 14, 0, 14, 9, 8, 5, 0, 0, 0, 40, 9, 2, 0, 0, 2, 9, 40, 0, 0, 2, 0, 0, 45, 2, 0, 49, 0, 2, 45, 0, 0, 2

Offset: 0

Douglas Stones (dssto1(AT)student.monash.edu.au), Sep 04 2004

			1; 1,1; 8,1,8; 9,8,8,9; ...

Cf. A003991, A098364, A098365, A098366.

A100829 Numbers that are a sum of two nonzero squares and not divisible by 17.

Original entry on oeis.org

2, 5, 8, 10, 13, 18, 20, 25, 26, 29, 32, 37, 40, 41, 45, 50, 52, 53, 58, 61, 65, 72, 73, 74, 80, 82, 89, 90, 97, 98, 100, 101, 104, 106, 109, 113, 116, 117, 122, 125, 128, 130, 137, 145, 146, 148, 149, 157, 160, 162, 164, 169, 173, 178, 180, 181, 185, 193, 194, 197

Offset: 1

Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Jan 06 2005

nonn

Cf. A000404, A098365.

filter:= proc(x) local F;
  if x mod 17 = 0 then return false fi;
  F:= ifactors(x)[2];
  if ormap(t -> t[1] mod 4 = 3 and t[2]::odd, F) then return false fi;
  ormap(t -> t[1] mod 4 = 1 or (t[1]=2 and t[2]::odd), F)
end proc:
select(filter, [$1..200]); # Robert Israel, Jun 17 2025

With[{upto=200},Select[Total/@Tuples[Range[Ceiling[Sqrt[upto]]]^2,2], Mod[ #,17]!=0&&#<=upto&]]//Union (* Harvey P. Dale, May 18 2019 *)

Definition corrected by Robert Israel, Jun 17 2025

cp's OEIS Frontend

A099178 Numbers which are the sum of two positive cubes and divisible by 17.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

A098364 Multiplication table of the digits of the square root of 2 read by antidiagonals.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

PARI

Formula

Extensions

A098366 Multiplication table of the digits of the cube root of 2 read by antidiagonals.

Views

Author

Keywords

Examples

Crossrefs

A098367 Multiplication table of the digits of the fourth root of 2 read by antidiagonals.

Views

Author

Keywords

Examples

Crossrefs

A100829 Numbers that are a sum of two nonzero squares and not divisible by 17.

Views

Author

Keywords

Crossrefs

Programs

Maple

Mathematica

Extensions